29 research outputs found
Isotropic Forms of Dynamics in the Relativistic Direct Interaction Theory
The Lagrangian relativistic direct interaction theory in the various forms of
dynamics is formulated and its connections with the Fokker-type action theory
and with the constrained Hamiltonian mechanics are established. The motion of
classical two-particle system with relativistic direct interaction is analysed
within the framework of isotropic forms of dynamics in the two- and
four-dimensional space-time. Some relativistic exactly solvable
quantum-mechanical models are also discussed.Comment: 49 pages, 12 figures, Latex2
Fokker-Type Confinement Models from Effective Lagrangian in Classical Yang-Mills Theory
Abelian potentials of pointlike moving sources are obtained from the
nonstandard theory of Yang--Mills field. They are used for the construction of
the time-symmetric and time-asymmetric Fokker-type action integrals describing
the dynamics of two-particle system with confinement interaction. The
time-asymmetric model is reformulated in the framework of the Hamiltonian
formalism. The corresponding two-body problem is reduced to quadratures. The
behaviour of Regge trajectories is estimated within the semiclassical
consideration.Comment: 40 pages, 8 figures, submit. to Internat. J. Modern Phys.
Solvable Two-Body Dirac Equation as a Potential Model of Light Mesons
The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular structure is found, for which the equation is exactly solvable. On this ground a relativistic potential model of light mesons is constructed and the mass spectrum is calculated. It is compared with experimental data
Confinement interaction in nonlinear generalizations of the Wick-Cutkosky model
We consider nonlinear-mediating-field generalizations of the Wick-Cutkosky
model. Using an iterative approach and eliminating the mediating field by means
of the covariant Green function we arrive at a Lagrangian density containing
many-point time-nonlocal interaction terms. In low-order approximations of
theory we obtain the usual two-current interaction as well as
a three-current interaction of a confining type. The same result is obtained
without approximation for a version of the dipole model. The transition to the
Hamiltonian formalism and subsequent canonical quantization is performed with
time non-locality taken into account approximately.
A relativistic three-particle wave equation is derived variationally by using
a three-particle Fock space trial state. The non-relativistic limit of this
equation is obtained and its properties are analyzed and discussed.Comment: 15 pages, 1 figure, LaTe
Large-j Expansion Method for Two-Body Dirac Equation
By using symmetry properties, the two-body Dirac equation in coordinate representation is reduced to the coupled pair of radial second-order differential equations. Then the large-j expansion technique is used to solve a bound state problem. Linear-plus-Coulomb potentials of different spin structure are examined in order to describe the asymptotic degeneracy and fine splitting of light meson spectra
Heuristic Models of Two-Fermion Relativistic Systems with Field-Type Interaction
We use the chain of simple heuristic expedients to obtain perturbative and
exactly solvable relativistic spectra for a family of two-fermionic bound
systems with Coulomb-like interaction. In the case of electromagnetic
interaction the spectrum coincides up to the second order in a coupling
constant with that following from the quantum electrodynamics. Discrepancy
occurs only for S-states which is the well-known difficulty in the bound-state
problem. The confinement interaction is considered too.
PACS number(s): 03.65.Pm, 03.65.Ge, 12.39.PnComment: 16 pages, LaTeX 2.0